SOLUTION: how many years will it take $5,500 to grow to $6,300 if it is invested at an annual rate of 2.5% compounded continuously?

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Question 812083: how many years will it take $5,500 to grow to $6,300 if it is invested at an annual rate of 2.5% compounded continuously?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
how many years will it take $5,500 to grow to $6,300 if it is invested at an annual rate of 2.5% compounded continuously?
A = Pert

A = final amount = 6300 
P = beginning amount = 5500
r = rate expressed as a decimal = 0.025
t = time in years = (the unknown)

               A = Pert 
  
Solve for t. Divide both sides by P

              A%2FP = ert  

Write an equivalent natural log equation using the rule that 
X = eY is equivalent to Y = ln(X)

              rt = ln%28A%2FP%29

Use the rule of logs ln%28X%2FY%29 = ln(X)-ln(Y)

              rt = ln(A)-ln(P)

Divide both sides by r

               t = %28ln%28A%29-ln%28P%29%29%2Fr

Now substitute the given values 

               t = %28ln%286300%29-ln%285500%29%29%2F0.025     

Put that in your TI-83 or TI-84 this way

(ln(6300)-ln(5500))/0.025

Press ENTER

Read 5.432061646 years or about 5 years and 5 months.

Edwin